In addition to the neutrino masses and DM mystery, the SM gauge symmetries cannot explain how different flavors of leptons distinguish each other and exhibit the observed mixing patterns. A promising ansatz which can potentially solves the flavor puzzle is to add an extra \(U(1)\)  gauge symmetry to SM and permit the three flavors of fermions transform nonuniversally under the new symmetry. On the other hand,
three right-handed(RH) neutrinos \(N_R\) s are usually considered as necessary ingredients of neutrino mass model. Then assuming family nonuniversal charges of \(N_R\) s, the resulting lepton flavor structure admits a number of anomaly-free solutions. Along this thought of idea, the \(U(1)_X\)  gauge symmetry with \(X\)  being the linear combinations of baryon number \(B\)  and individual lepton numbers \(L_\alpha \)  is frequently considered in various contexts. Well-known examples are \(B-3L_{\tau }\)[1]}, \( L_{\mu }-L_{\tau } \)[2]}, [3]}, [4]}, [5]}, \(B+3(L_e-L_\mu -L_\tau )\)[6]} etc.
In Ref.[7]}, the neutrino mass matrices containing two-zero-texture[8]}, [9]} or two-zero-cofactor structures[10]} are realized by applying the \(U(1)_{aB-\Sigma x_\alpha L_\alpha }\)  gauge symmetry to type-I seesaw scenario. In Ref.[11]}, more solutions are found in the type-I and/or-III seesaw framework. It is then natural to ask if the flavor-dependent \(U(1)\)  gauge symmetry is compatible with the scotogenic models and leads to predictive lepton mass textures. The first attempts was made in Ref.[12]}, where the \(U(1)_{L_{\mu }-L_{\tau }}\)  gauge symmetry was adopted to realize the type-C two-zero-texture structure[9]} in one-loop induced neutrino mass matrix. Note that this model is also possible to interpret the \(R_{K^{(*)}}\)  anomaly and AMS-02 positron excess [14]}.
However, the latest analysis points out that such texture structure is incompatible with the Planck 2018 bound on the sum of neutrino masses. i.e \(\Sigma m_i <0.12\) eV[15]}. One way out of this problem is to consider different \(U(1)\)  gauge symmetries. In Refs.[16]}, [17]}, other viable two-zero-texture structures are realized based on \(U(1)_{B-2L\alpha -L_{\beta }}\)  gauge symmetry.
